Knowledge of the primordial lithium abundance (Lip) tests and constrains models of big bang nucleosynthesis and may have implications for dark matter and the laws of physics. An apparent small dispersion in the Li abundances of field halo dwarfs had been predicted to result from differences in the Li depletion of models with rotationally induced mixing, and would imply a higher Lip than is observed today in these stars. However, this dispersion could also be explained by differential Galactic Li enrichment (from lower Lip) coupled with a halo age spread and/or incomplete mixing. To differentiate between these possibilities, we have obtained Keck/HIRES observations at R = 45,000 in one of the oldest and most metal-poor globular clusters, M92, where differential Li enrichment within the cluster is unlikely. We find some evidence for differences in the Li abundances of three otherwise apparently identical M92 subgiants in the Spite Li plateau. We provide evidence against cosmic-ray, supernova, and asymptotic giant branch star Li production as causing these Li differences, and suggest that different stellar surface Li depletion histories in these stars from a higher initial abundance is a more likely explanation (as is also the case for open clusters). This higher initial abundance may have been the Lip, or a combination of Lip plus significant pre-M92 Galactic Li. Implications are discussed.